The Sigma 50-500 mm is a big heavy lens and it should be used with a tripod or bipod if it doesn't have IS it is difficult to hold steady . Most of your pics show some blur. As for shooting perhaps you should set up the ISO rather than going auto and that will lighten and brighten the pic somewhat and in photo editing cut back on the contrast and saturation. Pehaps a circiular would come in handy. It's a great situation to be in to capture these wonderful moments. are you shooting from a blind and have the sun at your back.You have a deadly combination a lot of guys would like. I have Sony A550 wih a Siggy 4oo mm prime.